论文标题
基于Copula的分析集群网络中的广义友谊悖论
Copula-based analysis of the generalized friendship paradox in clustered networks
论文作者
论文摘要
社交网络的异质结构引起了各种有趣的现象。其中之一是友谊悖论，它平均而言，您的朋友的朋友比您多。它的概括称为广义友谊悖论（GFP），指出您的朋友的属性平均比您的属性更高。尽管通过经验分析和数值模拟成功地证明了GFP，但对GFP的分析，严格的理解在很大程度上尚未开发。最近，使用Copula方法获得了GFP在具有相关属性网络中的个体中的概率的分析解决方案，但通过假设基础网络的局部树结构[JO〜ET〜ET〜E，物理审查E〜 \ textbf {104}，104}，054301（2021）]。考虑到大多数社交网络中丰富的三角形，我们采用了一种葡萄藤方法，除了焦点个体与其邻居之间的相关性外，焦点个体邻居之间的属性相关结构都结合在一起。我们的分析方法有助于我们严格了解更通用的网络中的GFP，例如聚类网络和社交网络中其他相关有趣的现象。
A heterogeneous structure of social networks induces various intriguing phenomena. One of them is the friendship paradox, which states that on average your friends have more friends than you do. Its generalization, called the generalized friendship paradox (GFP), states that on average your friends have higher attributes than yours. Despite successful demonstrations of the GFP by empirical analyses and numerical simulations, analytical, rigorous understanding of the GFP has been largely unexplored. Recently, an analytical solution for the probability that the GFP holds for an individual in a network with correlated attributes was obtained using the copula method but by assuming a locally tree structure of the underlying network [Jo~et~al., Physical Review E~\textbf{104}, 054301 (2021)]. Considering the abundant triangles in most social networks, we employ a vine copula method to incorporate the attribute correlation structure between neighbors of a focal individual in addition to the correlation between the focal individual and its neighbors. Our analytical approach helps us rigorously understand the GFP in more general networks such as clustered networks and other related interesting phenomena in social networks.
